integral from a to b of g(y)-f(y)

解

\int_{a}^{b} g (y) - f (y) d y

\frac{g ( b ^{2} - a ^{2} )}{2} - \frac{f ( b ^{2} - a ^{2} )}{2}

解答ステップ

\int_{a}^{b} g y - f y d y

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{a}^{b} g y d y - \int_{a}^{b} f y d y

\int_{a}^{b} g y d y = \frac{g ( b ^{2} - a ^{2} )}{2}

\int_{a}^{b} f y d y = \frac{f ( b ^{2} - a ^{2} )}{2}

= \frac{g ( b ^{2} - a ^{2} )}{2} - \frac{f ( b ^{2} - a ^{2} )}{2}